The other factor is the size of the generator vs the rating of the lathe - kw, horsepower, or whatever units you use. The closer the lathe power demand is to the rating of the generator, the greater are the risks of some kind of problem. If the generator is significantly larger than the lathe, I would expect the combination to work just fine.
By the way, Colin's suggestion about putting a plastic shield in front of the lathe is very good. I don't think I have ever seen a demo setup here in the US that doesn't have a plastic shield. We have entirely too many tort lawyers who make their living exploiting accidents.
